An inversion process in geophysics data processing usually, and in the case of this document as well, refers to the process of transforming seismic reflection data into a quantitative rock-property description of a reservoir in the form of a subsurface earth model. Such a model needs three parameters, which are density (ρ), P-wave velocity (VP) and S-wave velocity (VS) to describe it, if the model is assumed to be isotropic. Additional parameters are needed in a more general subsurface model that includes anisotropy and attenuation. There are many techniques used in inversion at seismic resolution, such as post-stack or pre-stack AVO inversion and Full-Waveform Inversion (FWI).
It is well known that PP reflection (P-wave down/P-wave up) at normal incident angle is largely determined by the acoustic impedance Ip=ρVp. In order to estimate Ip from seismic data, it is usually sufficient to consider only P-wave propagation in FWI to save processing time. For that purpose, modeling of wave propagation depends only on ρ and Vp. However, Ip alone is not always a good indicator of reservoir rocks and types. It is know that fluid types can be better retrieved from elastic parameters such as VP/VS. As a result, multi-parameter inversion for both acoustic and elastic parameters has become desirable, perhaps almost necessary, in reservoir characterization.
Multi-parameter inversion through elastic FWI has a unique role in delineating reservoir characters as it is based on accurate modeling of elastic wave propagation. Elastic FWI is a highly expensive process for two main reasons. First, finite difference modeling becomes far more expensive than under the acoustic (P-wave only) assumption due to denser computational grids needed for computer simulation of shear wave propagation. Second, multi-parameter inversion requires many more iterations than acoustic FWI to achieve convergence and reduce crosstalk between different parameters. In reservoir characterization, the most important parameters to describe rock properties are acoustic impedance Ip and the velocity ratio Vp/VS. Therefore, there is a need for an FWI method than can robustly invert for Ip and Vp/VS in a small number of iterations (preferably ˜10) to make it practical in business applications such as reservoir characterization and velocity model building.
There are a wide variety of methods to estimate rock properties from seismic data. The procedure proposed by Hampson et al. (2005) represents a typical workflow in pre-stack AVO inversion. In their workflow, IP, IS and density are estimated simultaneously based on AVO in angle gathers and the Aki-Richards equations (Aki and Richards, 2002). Their approach is based on linearized approximation for reflectivity instead of the iterative process of simulating elastic waves and matching waveforms. Computational cost is therefore much cheaper in pre-stack inversion due to the linearized approximation. In contrast, elastic FWI, although a much more expensive process, has the potential to generate superior results.